Abstract: Allocative efficiency is fundamentally a spatial problem—the distribution of shot attempts within a lineup is highly dependent on court location. Despite the importance of spatial context, there are very few allocative efficiency analyses which have explicitly accounted for this critical factor. Our unique contribution with this work is a method to analyze allocative efficiency spatially.
The main idea behind our approach is to compare a player’s field goal percentage (FG%) to his field goal attempt rate in context of his four teammates in any given lineup. To this end, we build Bayesian hierarchical models to estimate player field goal percentages (FG%) and field goal attempt (FGA) rates at every location on the floor using publicly available NBA shot location data. We next determine the rank of each player’s FG% and FGA relative to his four teammates at every location in the half-court. Finally, by pairing each player’s lineup-specific FGA rankings with their corresponding FG% rankings, we can explore the relationship between FG% rank and FGA rank and detect areas where the lineup exhibits inefficient allocation of shots.
We further analyze the impact that deviations from optimality have on a lineup’s overall efficiency. We develop a measure called lineup points lost (LPL), which we define as the difference in expected points between the observed allocation of shot attempts and the optimal redistribution. Using these metrics, we can quantify how many points are being lost through inefficient spatial lineup shot allocation, visualize where they are being lost, and identify which players are responsible.